**MSC:**- 62E15 Exact distribution theory
- 62E17 Approximations to distributions (nonasymptotic)

generalized chi-square distributions are numerically evaluated based upon

new geometric representation formulas for these distributions. Using

standard numerical methods exact quantiles can be calculated then.

Explicit quantile approximation formulas and algorithms are deduced from an

asymptotic expansion for related probabilities of large deviations. Several

numerical studies compare the present results with results of other

authors.